Unconventional superconductivity? The strange case of - PowerPoint Presentation

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Unconventional superconductivity? The strange case of CeCu2Si2

F. Steglich+,§,# + Max Planck Institute for Chemical Physics of Solids (MPI CPfS), Dresden, Germany § Center for Correlated Matter, Zhejiang University (CCM, ZJU), Hangzhou, China # Institute of Physics, Chinese Academy of Sciences (IOP, CAS), Beijing, China

Collaboration

Neutron

scattering

, STM/STS

J

. Arndt, O.

Stockert

, S

. Wirth (MPI

CPS, Dresden)

Penetration

depth

,

specific

heat

G

. M. Pang, M. Smidman,

J. L. Zhang, L.

Jiao

, Z. Weng. Y. Chen, W. Jiang,

Y. Zhang, W. Xie, H. Lee, H. Q. Yuan (CCM, ZJU Hangzhou)

Single

crystals

H. S.

Jeevan

, P. Gegenwart (U. Augsburg):

Ce

Cu

2

Si

2

C.

Krellner

(U. Frankfurt):

Yb

Rh

2

Si

2

Theory

G

. Zwicknagl (TU Braunschweig

)

J. X. Zhu (LANL)

E

. M. Nica, R. Yu, Q. Si (

RCQM,

Rice U.,

Houston, TX)

Phase diagrams of unconventional superconductors

Cuprates

,

……

Organic charge-transfer salts,

Fe-based compounds,

Spin, charge, orbital, lattice excitations

B. Keimer et al., Nature (2015)

Heavy fermion metals separation of scales: λSO(103-104K), ΔCF(102K), TK ,TRKKY(10 K), Tc (1 K)↷ spin - / charge - fluctuations

Quantum

critical

paradigm

: AF QCP in clean,

stoichiom

. HF

metal

↷

unconv

. SC!

Explore

Ce

Cu

2

Si

2

&

Yb

Rh

2

Si

2

!

Ce

Cu2Si2Homogeneity range: ~ 1% Cu/Si site exchange ↑

←

Cu deficit true stoichiometry Cu excess

→

ΔCF ≫

kBTK∽ JK ≃ 2 meV S

eff = 1/2Pairing interactions ≤ IRKKY ≃ JK

Quantum

criticality in CeCu2Si2χ‘‘T3/2 = f (

ħ

ω

/(k

BT)3/2)

[J. Arndt et al., PRL 106, 246401 (’11)]Δρ ~ T3/2, γ

= γ0 – bT1/2 [P. Gegenwart et al., PRL 81, 1501 (‘98)]

3D-SDW QCPB - p phase diagram[E. Lengyel et al., PRL 107, 057001 (‘11)S-type crystal in low-T n-stateA/S-type crystal

(1-band) d - wave superconductivity in CeCu2Si

2 Cu

NQR

K.

Fujiwara

et al., JPSJ 77,

123711 (‘08)cf. alsoK. Ishida et al., PRL 82, 5353 (‘99)

T

= Tc : no Hebel-Slichter peak T < Tc : 1/T1 ~ T3 d - wave SC, nodes of Δ(k)strong coupling d – wave SC: 2

Δ

0

/

k

B

T

c

= 5

[

weak

coupling

d

-

wave

SC:

2

Δ

0

/

k

B

T

c

= 4.3]

T - dependence of specific heat for Ce

Cu2Si2 [S. Kittaka et al., PRL 112, 067002 (2014)]T. Takenaka et al., PRL

119

, 077001 (2017):

T

c insensitive against el-irradiation Fully gapped as T → 0

CeCu2Si2: Two-band s-wave superconductor without sign-changing Δ(k) [BCS SC] ↷

T -

dependence of superfluid density ϱs(T) in CeCu2

Si

2

[G. M. Pang et al.,

PNAS 115, 5343 (2018)]

Harmless disorder in

CeCu2Si2Tc ≃ 0.6 K

insensitive

against variations of

ϱ0 : ϱ0

(“S”) ≃ 4 ϱ0(“A/S”) G. M. Pang et al., PNAS 115, 5343 (2018)•

Cu/Si interchange < 1 % (change of ϱ0)

harmless• shift from lattice sites into interstitials (el. irradiation)

Cu

-site: xc ≃ 1 at% for

Mn

,

Pd

, Rh (Δ

TK ≃ + 7 mK)Atomic substitution in CeCu2Si2

[H. Spille, U. Rauchschwalbe, FS, Helv. Phys. Acta 56, 165 (1983); H. Q. Yuan, F. M. Grosche, M. Deppe et al., Science 302, 2104 (2003)]

Ce-site (size-dependence): ΔrCe-M [Å] xc[at%] Sc + 0.28 1 Y + 0.13 6 Th + 0.06 20 La - 0.03 10 site dependenceIncompatible with s++ pairing[P. W. Anderson, Phys. Rev. Lett. 3, 325 (1959)]

Si

-site:

x

c

:

(15 – 20) at%

for

Ge

x

=

0.1

:

l

mfp

>

ξ

;

0.25

:

l

mfp< ξ

Nature of the AF (A) phase in CeCu2Si2[O. Stockert

, G. Zwicknagl et al., PRL 92, 136401 (2004)]Observation of AF satellite peaksin (hhl) scattering planeLong-range AF order with propagation vector QAF = (0.215 0.215 0.530) at T

= 50 mK

T

N

 0.8 Km

0 ≲ 0.1 B

Nesting of large Fermi surface in Ce

Cu2Si2[O. Stockert, G. Zwicknagl et al., PRL 92, 136401 (2004)]Fermi surface of heavy quasiparticles calculated with renormalized band method, m*

 500 m

e

warped columns along tetragonal axis

Static susceptibility in (hhl

) planeNesting for incommensurate wave vectorτ ≃ (0.21 0.21 0.55) ≃ QAF

Fermi surface unstable with respect to formation of spin-density wave

k =

QAFSuperconductivity in CeCu2Si2 near a (3D) SDW QCP[O. Stockert et al., Nature Phys. 7

, 119 (2011)]

“

slowing

down“

Δ

Г

~ Tαα = 1.38 ∓ 0.16(3D SDW) α = 1.5

[J. Arndt et al.,

PRL

106

, 246401 (2011)]

B

= 2 T:

quasielastic

line

, HWHM

↷

T

K

B

= 0:

spin

gap

below

peak

at 0.2

meV

Propagating ‘paramagnon‘ mode (not a ‘spin

r

esonance

‘

)

at

3.9

k

B

T

c

[<

2

Δ

1

(

T

=0)

≃ 5

k

B

T

c

]

↷

No s - wave superconductor

s

++

: doesn‘t show

sign change in Δ(k)! no onsite pairing of HFs: Ueff ≃ kB

TK!s+- : nesting wavevector different from QAF

can‘t explain spin resonance!↷ “d+d band - mixing“ Cooper pairing [E. Nica et al. ‘16]

Large

INS intensity in

sc state

at

k

=

Q

AF

and

low

ħ

ω

,

i.e.,

coherence factor {1-cos[

Φ

(

k

)

]} ≃ 2,

where

Φ(k) is the phase difference in Δ(k) between k & k + Q

AF

,

↷

Φ

(

k

) ≃

π

↷

sign

change

of

Δ

(

k

)

along

Q

AF

inside

dominating

HF

band

!

Inelastic

n-

scattering

reveals

sign

change

of

Δ

(

k

)

[O. Stockert et al.,

Nature Phys.

7

, 119 (2011)]

2 - band

d

-

wave

SC

without

nodes

,

cf.

3

He -

B

phase

(

p

-

wave

pairing

)

Band-mixing ‘

d+d ‘ pairing model: explains ALL data [(E.M. Nica, R. Yu and Q. Si., npj Quantum Materials (2017) 2:24]

Intraband

:

~ d

x

2-y2Interband:~ dxy Finite gap

on whole Fermi surface; Sign-change of intra-band pairing (within warped cylinders).Band basis:

Yb

Rh2Si2: Emergence of SC by

nuclear

AF

order

[Science 351, 485 (2016)]

a.TN

≃ 70 mK: 4f - electr. AF order TB ≃ 10 mK: increase of M(T) TA ≃ 2 mK: new phase transition

b.

T

c

≃

2

mK

:

SC [

χ

’’(

T

):

1

st

order

!)]

c.

T

A

≃

2 mK: “

A

- phase

“

d.

B

<

4 mT:

T

A

>

T

c

TB:

small sc regions, Tc: large superconducting shielding

T

<

T

c = 2 mK: large superconducting

shielding signal in zfc - MDC(T) and χ

AC(T)T < TB = 10 mK: partial sc shielding – concurs with increasing fc -

M

DC

(

T

)

which

is

illustrating

decreasing

primary

staggered

magnetization

,

m

AF

,

due

to

competing

nuclear

(

A

-phase)

short

-range

correlations

(

nuclear

spin

entropy

!)

Summary

YbRh2Si2⦁ MDC(T), χAC(

T

)

prove

:

(bulk) heavy-fermion SC at B < 4 mT

⦁ YbRh2Si

2: - SC near (4f – “Mott – type“) transition (T = 0), like CeRhIn5 at p > 0

-

both systems form

link

between

(≃ 50)

HFSCs

and

cuprates, organics, …

near

true Mott

transition

B

c2

‘

≃ 25 T/K

from

Meissner

m

easurements

(same from shielding

measurements)

E. Schubert et al. (2016)

Quantum Critical Paradigm

: Unconventional SC at HF AF QCPs

Ce

Pd

2

Si

2N. D. Mathur et al., Nature

394, 39 (1998)● CeCu2Si2: fully gapped 2 - band d - wave superconductor ● YbRh2Si2:

HF SC, Tc = 2 mK● Unconventional SC near AF QCPs: robust phenomenonFurther reading: M. Smidman et al., Phil. Mag. 98, 2930 (2018)